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Question

In the given figure, AB=AC and GBC=HCB=90.
Which of the following statements is true?

A
AG = AB and BG = CH
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B
BG = CB and AG = AH
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C
BG = CH and AG = AH
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D
BAC=120
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Solution

The correct option is C BG = CH and AG = AH

(i) ΔBAC is isosceles ….. (given)

(ii) ABC=ACB=x (say) (base angles of an isosceles triangle)

(iii) GBC=HCB=90 .. (given)

(iv) GBA=HCA=90x

In ΔGBA and ΔHCA

(v) GBA=HCA (from (iv))

(vi) AB=AC …(given)

(vii) GAB=HAC .….(vertically opposite angles are equal)

(viii) ΔGBAΔHCA …… (ASA postulate)

BG=CH and AG=AH ...(CPCT)


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